Finite Group Databasebeta

← C29×#10991 #20305891

Subgroups — C29×#10991 #20305891

Order 7424.

3122 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×#120C211yesmaximal, characteristic
2C22×C29×#99C211yesmaximal, characteristic, complemented
3C29×#2308C211yesmaximal, characteristic, complemented
4C2×C29×#379C212yesmaximal, complemented
5C2×C29×#342C212yesmaximal, complemented
6C26×C29C2211yescharacteristic
7C23×D4×C29—21no—
8C23×D4×C29C2211yescharacteristic
9C2×C29×#120—24no—
10C2×C29×#120—22no—
11C2×C29×#120—24no—
12C2×C29×#120C414yescomplemented
13C22×C22⋊C4×C29—21no—
14C22×C22⋊C4×C29—24no—
15C22×C22⋊C4×C29C2212yes—
16C22×C22⋊C4×C29C2212yes—
17C22×C22⋊C4×C29C2211yescharacteristic
18C2×C29×#99—22no—
19C2×C29×#99—24no—
20C29×#386—24no—
21C29×#381—21no—
22C29×#379—24no—
23C29×#379—21no—
24C29×#379—24no—
25C29×#342—24no—
26C25×C29—22no—
27C25×C29—21no—
28C25×C29—21no—
29C25×C29—22no—
30C25×C29—22no—
31C25×C29—22no—
32C25×C29—22no—
33C25×C29—48no—
34C25×C29C2×C412yes—
35C25×C29D414yes—
36C25×C29D411yescharacteristic
37C25×C29C2311yescharacteristic
38C22×D4×C29—28no—
39C22×D4×C29—24no—
40C22×D4×C29—22no—
41C22×D4×C29—22no—
42C22×D4×C29—22no—
43C22×D4×C29—22no—
44C22×D4×C29—22no—
45C22×D4×C29—22no—
46C22×D4×C29—48no—
47C22×D4×C29C2×C412yes—
48C22×D4×C29D412yes—
49C23×C4×C29—21no—
50C23×C4×C29—22no—
51C23×C4×C29D411yescharacteristic
52C23×C4×C29D414yescomplemented
53C29×#120—216no—
54C29×#120—28no—
55C29×#120—28no—
56C2×C22⋊C4×C29—28no—
57C2×C22⋊C4×C29—22no—
58C2×C22⋊C4×C29—21no—
59C2×C22⋊C4×C29—24no—
60C2×C22⋊C4×C29—22no—
61C2×C22⋊C4×C29—22no—
62C2×C22⋊C4×C29—22no—
63C2×C22⋊C4×C29—22no—
64C2×C22⋊C4×C29—216no—
65C2×C22⋊C4×C29—22no—
66C2×C22⋊C4×C29—22no—
67C2×C22⋊C4×C29—22no—
68C2×C22⋊C4×C29—22no—
69C2×C22⋊C4×C29—22no—
70C2×C22⋊C4×C29—22no—
71C2×C22⋊C4×C29—22no—
72C2×C22⋊C4×C29—24no—
73C2×C22⋊C4×C29—416no—
74C2×C22⋊C4×C29C2×C412yes—
75C2×C22⋊C4×C29D414yes—
76C2×C22⋊C4×C29D414yescomplemented
77C29×#99—28no—
78C29×#95—24no—
79C24×C29—216no—
80C24×C29—28no—
81C24×C29—22no—
82C24×C29—24no—
83C24×C29—24no—
84C24×C29—24no—
85C24×C29—24no—
86C24×C29—22no—
87C24×C29—24no—
88C24×C29—24no—
89C24×C29—22no—
90C24×C29—21no—
91C24×C29—24no—
92C24×C29—24no—
93C24×C29—22no—
94C24×C29—21no—
95C24×C29—48no—
96C24×C29—416no—
97C24×C29—44no—
98C24×C29—48no—
99C24×C29—44no—
100C24×C29—416no—
101C24×C29—48no—
102C24×C29—416no—
103C24×C29—416no—
104C24×C29—416no—
105C24×C29—44no—
106C24×C29—41no—
107C24×C29—41no—
108C24×C29—42no—
109C24×C29—42no—
110C24×C29—42no—
111C24×C29—42no—
112C24×C29—41no—
113C24×C29—41no—
114C24×C29—42no—
115C24×C29—42no—
116C24×C29C22⋊C414yescomplemented
117C24×C29C22⋊C412yescomplemented
118C24×C29C22×C411yescharacteristic
119C24×C29C2×D411yescharacteristic
120C24×C29C2×D412yes—
121C24×C29C2×D412yes—
122C24×C29C2×D411yescharacteristic
123C24×C29C2×D412yes—
124C24×C29C2×D412yes—
125C24×C29#4112yes—
126C24×C29#4112yes—
127C2×D4×C29—216no—
128C2×D4×C29—22no—
129C2×D4×C29—22no—
130C2×D4×C29—24no—
131C2×D4×C29—24no—
132C2×D4×C29—24no—
133C2×D4×C29—22no—
134C2×D4×C29—24no—
135C2×D4×C29—22no—
136C2×D4×C29—416no—
137C2×D4×C29—432no—
138C2×D4×C29—42no—
139C2×D4×C29—42no—
140C2×D4×C29—42no—
141C2×D4×C29—42no—
142C2×D4×C29—42no—
143C2×D4×C29—42no—
144C2×D4×C29—42no—
145C2×D4×C29—42no—
146C22×C4×C29—22no—
147C22×C4×C29—22no—
148C22×C4×C29—24no—
149C22×C4×C29—21no—
150C22×C4×C29—22no—
151C22×C4×C29—21no—
152C22×C4×C29—24no—
153C22×C4×C29—24no—
154C22×C4×C29—24no—
155C22×C4×C29—24no—
156C22×C4×C29—44no—
157C22×C4×C29—48no—
158C22×C4×C29—48no—
159C22×C4×C29—42no—
160C22×C4×C29—42no—
161C22×C4×C29C22⋊C412yescomplemented
162C22⋊C4×C29—216no—
163C22⋊C4×C29—22no—
164C22⋊C4×C29—24no—
165C22⋊C4×C29—24no—
166C22⋊C4×C29—24no—
167C22⋊C4×C29—432no—
168C22⋊C4×C29—42no—
169C22⋊C4×C29—42no—
170C22⋊C4×C29—42no—
171C22⋊C4×C29—42no—
172C22⋊C4×C29—42no—
173C22⋊C4×C29—42no—
174C22⋊C4×C29—84no—
175C22⋊C4×C29C22⋊C414yescomplemented
176#10991C2911yesmaximal, characteristic, direct product factor, Sylow
177C23×C29—28no—
178C23×C29—24no—
179C23×C29—216no—
180C23×C29—28no—
181C23×C29—216no—
182C23×C29—216no—
183C23×C29—216no—
184C23×C29—24no—
185C23×C29—28no—
186C23×C29—22no—
187C23×C29—22no—
188C23×C29—22no—
189C23×C29—48no—
190C23×C29—42no—
191C23×C29—42no—
192C23×C29—44no—
193C23×C29—44no—
194C23×C29—44no—
195C23×C29—44no—
196C23×C29—44no—
197C23×C29—44no—
198C23×C29—416no—
199C23×C29—48no—
200C23×C29—48no—
201C23×C29—48no—
202C23×C29—48no—
203C23×C29—416no—
204C23×C29—416no—
205C23×C29—48no—
206C23×C29—416no—
207C23×C29—48no—
208C23×C29—416no—
209C23×C29—416no—
210C23×C29—416no—
211C23×C29—416no—
212C23×C29—44no—
213C23×C29—48no—
214C23×C29—48no—
215C23×C29—416no—
216C23×C29—48no—
217C23×C29—416no—
218C23×C29—42no—
219C23×C29—42no—
220C23×C29—44no—
221C23×C29—44no—
222C23×C29—44no—
223C23×C29—44no—
224C23×C29—44no—
225C23×C29—48no—
226C23×C29—42no—
227C23×C29—42no—
228C23×C29—44no—
229C23×C29—82no—
230C23×C29—84no—
231C23×C29C2×C22⋊C411yescharacteristic
232C23×C29C2×C22⋊C411yescharacteristic
233C23×C29C2×C22⋊C411yescharacteristic
234C23×C29C4×D412yes—
235C23×C29C4×D412yes—
236C23×C29#12012yes—
237C23×C29#12012yes—
238C23×C29#12012yes—
239C23×C29#12011yescharacteristic
240C23×C29#12011yescharacteristic
241C23×C29#12112yes—
242C23×C29#12112yes—
243C23×C29#12112yes—
244C23×C29#12112yes—
245C23×C29#12112yes—
246C23×C29#12112yes—
247C23×C29#12311yescharacteristic
248C23×C29#12311yescharacteristic
249C23×C29#12312yes—
250C23×C29#12412yes—
251C23×C29#12712yes—
252D4×C29—432no—
253D4×C29—44no—
254D4×C29—44no—
255D4×C29—44no—
256D4×C29—44no—
257C2×C4×C29—22no—
258C2×C4×C29—24no—
259C2×C4×C29—22no—
260C2×C4×C29—22no—
261C2×C4×C29—44no—
262C2×C4×C29—48no—
263C2×C4×C29—42no—
264C2×C4×C29—42no—
265C2×C4×C29—48no—
266C2×C4×C29—48no—
267C2×C4×C29—44no—
268C2×C4×C29—44no—
269C2×C4×C29—48no—
270C2×C4×C29—84no—
271C2×C4×C29—84no—
272C2×C4×C29—84no—
273C22×#120C2×C2911yescharacteristic
274C22×#99C2×C2911yescharacteristic, complemented
275#2308C2×C2911yescharacteristic, complemented
276C2×#379C2×C2912yescomplemented
277C2×#342C2×C2912yescomplemented
278C22×C29—22no—
279C22×C29—24no—
280C22×C29—24no—
281C22×C29—22no—
282C22×C29—24no—
283C22×C29—24no—
284C22×C29—24no—
285C22×C29—24no—
286C22×C29—24no—
287C22×C29—24no—
288C22×C29—28no—
289C22×C29—216no—
290C22×C29—41no—
291C22×C29—41no—
292C22×C29—42no—
293C22×C29—42no—
294C22×C29—41no—
295C22×C29—42no—
296C22×C29—42no—
297C22×C29—42no—
298C22×C29—41no—
299C22×C29—42no—
300C22×C29—44no—
301C22×C29—416no—
302C22×C29—48no—
303C22×C29—48no—
304C22×C29—416no—
305C22×C29—416no—
306C22×C29—416no—
307C22×C29—44no—
308C22×C29—48no—
309C22×C29—44no—
310C22×C29—416no—
311C22×C29—44no—
312C22×C29—42no—
313C22×C29—82no—
314C22×C29—84no—
315C22×C29—84no—
316C22×C29#37911yescharacteristic
317C22×C29#38611yescharacteristic
318C22×C29#38612yes—
319C22×C29#38611yescharacteristic
320C22×C29#39012yes—
321C22×C29#39212yes—
322C22×C29#39212yes—
323C22×C29#39412yes—
324C22×C29#39412yes—
325C22×C29B(4,𝔽2)14yes—
326C4×C29—44no—
327C4×C29—42no—
328C4×C29—84no—
329C4×C29—84no—
330C26C22×C2911yescharacteristic
331C23×D4—21no—
332C23×D4C22×C2911yescharacteristic
333C2×#120—24no—
334C2×#120—22no—
335C2×#120—24no—
336C2×#120C4×C2914yescomplemented
337C22×C22⋊C4—21no—
338C22×C22⋊C4—24no—
339C22×C22⋊C4C22×C2912yes—
340C22×C22⋊C4C22×C2912yes—
341C22×C22⋊C4C22×C2911yescharacteristic
342C2×#99—22no—
343C2×#99—24no—
344#386—24no—
345#381—21no—
346#379—21no—
347#379—24no—
348#379—24no—
349#342—24no—
350C2×C29—21no—
351C2×C29—22no—
352C2×C29—22no—
353C2×C29—21no—
354C2×C29—22no—
355C2×C29—22no—
356C2×C29—22no—
357C2×C29—48no—
358C2×C29—82no—
359C2×C29#143811yescharacteristic
360C2×C29#188912yes—
361C2×C29#202114yes—
362C25—22no—
363C25—21no—
364C25—21no—
365C25—22no—
366C25—22no—
367C25—22no—
368C25—22no—
369C25—48no—
370C25C2×C4×C2912yes—
371C25D4×C2914yes—
372C25D4×C2911yescharacteristic
373C25C23×C2911yescharacteristic
374C22×D4—28no—
375C22×D4—24no—
376C22×D4—22no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—22no—
382C22×D4—48no—
383C22×D4C2×C4×C2912yes—
384C22×D4D4×C2912yes—
385C23×C4—21no—
386C23×C4—22no—
387C23×C4D4×C2911yescharacteristic
388C23×C4D4×C2914yescomplemented
389#120—216no—
390#120—28no—
391#120—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—216no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—416no—
410C2×C22⋊C4C2×C4×C2912yes—
411C2×C22⋊C4D4×C2914yes—
412C2×C22⋊C4D4×C2914yescomplemented
413#99—28no—
414#95—24no—
415C29#1099111yescharacteristic, direct product factor, Sylow
416C24—216no—
417C24—28no—
418C24—22no—
419C24—24no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—22no—
424C24—24no—
425C24—21no—
426C24—24no—
427C24—22no—
428C24—24no—
429C24—24no—
430C24—22no—
431C24—21no—
432C24—48no—
433C24—416no—
434C24—44no—
435C24—48no—
436C24—44no—
437C24—416no—
438C24—416no—
439C24—48no—
440C24—416no—
441C24—416no—
442C24—44no—
443C24—41no—
444C24—41no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—41no—
450C24—41no—
451C24—42no—
452C24—42no—
453C24C22⋊C4×C2914yescomplemented
454C24C22⋊C4×C2912yescomplemented
455C24C22×C4×C2911yescharacteristic
456C24C2×D4×C2911yescharacteristic
457C24C2×D4×C2912yes—
458C24C2×D4×C2912yes—
459C24C2×D4×C2911yescharacteristic
460C24C2×D4×C2912yes—
461C24C2×D4×C2912yes—
462C24#41×C2912yes—
463C24#41×C2912yes—
464C2×D4—216no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—22no—
473C2×D4—416no—
474C2×D4—432no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—42no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—44no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4C22⋊C4×C2912yescomplemented
499C22⋊C4—216no—
500C22⋊C4—22no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—432no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—84no—
512C22⋊C4C22⋊C4×C2914yescomplemented
513C23—28no—
514C23—24no—
515C23—216no—
516C23—216no—
517C23—28no—
518C23—216no—
519C23—216no—
520C23—24no—
521C23—28no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—48no—
526C23—42no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—42no—
531C23—44no—
532C23—44no—
533C23—48no—
534C23—48no—
535C23—416no—
536C23—416no—
537C23—48no—
538C23—416no—
539C23—44no—
540C23—416no—
541C23—48no—
542C23—48no—
543C23—48no—
544C23—416no—
545C23—416no—
546C23—416no—
547C23—416no—
548C23—44no—
549C23—48no—
550C23—48no—
551C23—416no—
552C23—48no—
553C23—416no—
554C23—48no—
555C23—42no—
556C23—42no—
557C23—44no—
558C23—44no—
559C23—44no—
560C23—44no—
561C23—44no—
562C23—44no—
563C23—42no—
564C23—42no—
565C23—82no—
566C23—84no—
567C23C2×C22⋊C4×C2911yescharacteristic
568C23C2×C22⋊C4×C2911yescharacteristic
569C23C2×C22⋊C4×C2911yescharacteristic
570C23C4×D4×C2912yes—
571C23C4×D4×C2912yes—
572C23C29×#12012yes—
573C23C29×#12012yes—
574C23C29×#12012yes—
575C23C29×#12011yescharacteristic
576C23C29×#12011yescharacteristic
577C23C29×#12112yes—
578C23C29×#12112yes—
579C23C29×#12112yes—
580C23C29×#12112yes—
581C23C29×#12112yes—
582C23C29×#12112yes—
583C23C29×#12311yescharacteristic
584C23C29×#12311yescharacteristic
585C23C29×#12312yes—
586C23C29×#12412yes—
587C23C29×#12712yes—
588D4—432no—
589D4—44no—
590D4—44no—
591D4—44no—
592D4—44no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—48no—
598C2×C4—44no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—48no—
602C2×C4—48no—
603C2×C4—48no—
604C2×C4—44no—
605C2×C4—44no—
606C2×C4—84no—
607C2×C4—84no—
608C2×C4—84no—
609C22—24no—
610C22—24no—
611C22—24no—
612C22—24no—
613C22—24no—
614C22—24no—
615C22—22no—
616C22—24no—
617C22—24no—
618C22—22no—
619C22—28no—
620C22—216no—
621C22—41no—
622C22—41no—
623C22—42no—
624C22—42no—
625C22—41no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—41no—
630C22—42no—
631C22—44no—
632C22—416no—
633C22—48no—
634C22—48no—
635C22—416no—
636C22—416no—
637C22—416no—
638C22—44no—
639C22—44no—
640C22—416no—
641C22—48no—
642C22—42no—
643C22—44no—
644C22—82no—
645C22—84no—
646C22—84no—
647C22C29×#37911yescharacteristic
648C22C29×#38611yescharacteristic
649C22C29×#38612yes—
650C22C29×#38611yescharacteristic
651C22C29×#39012yes—
652C22C29×#39212yes—
653C22C29×#39212yes—
654C22C29×#39412yes—
655C22C29×#39412yes—
656C22C29×B(4,𝔽2)14yes—
657C4—44no—
658C4—42no—
659C4—84no—
660C4—84no—
661C2—21no—
662C2—22no—
663C2—22no—
664C2—21no—
665C2—22no—
666C2—22no—
667C2—22no—
668C2—48no—
669C2—82no—
670C2C29×#143811yescharacteristic
671C2C29×#188912yes—
672C2C29×#202114yes—
subgroupG/H
center, socleC23×C29#120
commutatorC24C22×C4×C29
Frattini, cosocleC25C23×C29
prime radicalC22×C29×#120C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C25×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×C29×#99C2semidirect
3. C29×#2308C2semidirect
4. C2×C29×#379C2semidirect
5. C2×C29×#342C2semidirect
12. C2×C29×#120C4semidirect
52. C23×C4×C29D4semidirect
76. C2×C22⋊C4×C29D4semidirect
116. C24×C29C22⋊C4semidirect
117. C24×C29C22⋊C4semidirect
161. C22×C4×C29C22⋊C4semidirect
175. C22⋊C4×C29C22⋊C4semidirect
176. #10991C29direct (N × H)
274. C22×#99C2×C29semidirect
275. #2308C2×C29semidirect
276. C2×#379C2×C29semidirect
277. C2×#342C2×C29semidirect
336. C2×#120C4×C29semidirect
388. C23×C4D4×C29semidirect
412. C2×C22⋊C4D4×C29semidirect
415. C29#10991direct (N × H)
453. C24C22⋊C4×C29semidirect
454. C24C22⋊C4×C29semidirect
498. C22×C4C22⋊C4×C29semidirect
512. C22⋊C4C22⋊C4×C29semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C29×#1202
C22×C29×#992
C29×#23082
C2×C29×#3792
C2×C29×#3422
#1099129